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Methods for Accurate Measurement of the Response of Photomultiplier Tubes and Intensity of Light Pulses J. T. M. de Haas and P. Dorenbos, Member, IEEE
Abstract—Three different methods to determine accurately the intensity of weak light pulses measured with various photomultiplier tubes are presented. The methods rely on a precise determination of the response of the PMTs to the detection of a single photon. 10 kHz LED pulses attenuated to a level where on average to 30 photons are detected per pulse were used. For , the unknown value of weak intensity light pulses with can be obtained by fitting measured pulse height spectra employing these single photon response spectra. For higher intensity pulses, methods based on the position and/or the fractional variance of the recorded pulse height spectra will be used. The single photon response spectra provide information on the performance of the tested PMTs.
= 0 02
8
Index Terms—Photomultiplier tubes, scintillator, single electron response.
I. INTRODUCTION
P
HOTOMULTIPLIER TUBEs (PMTs) are used to monitor continuous low level light sources, weak light pulses, or for single photon counting. One may use the PMTs to simply count the number of pulses, one may use it for timing, or to obtain an absolute measure of the number of photons contained within weak light pulses. This latter aspect is particularly important for scintillation spectroscopy. Scintillation flashes typically contain 10,000 to 50,000 photons when 1 MeV of ionizing energy is deposited in the scintillator. The flash has a decaying intensity with a time constant that may vary from a few ns to several microseconds. To determine the absolute number of photons within a pulse an accurate calibration of the PMT is needed. A generally adopted method is to compare the response of the photomultiplier tube to a scintillation flash with the response of the PMT to the detection of one single photon. This method introduced by Bertolaccini et al. [1] seems quite straightforward but in practice is not trivial. The problem is to obtain a reliable single photon response spectrum of the PMT at the supply voltage used for scintillation detection. Simply recording the dark count spectrum does not provide the correct single photon response spectrum [2]. Bellamy et al. [3] approximates by a Gaussian function, and Dossi et al. [2] by a Gaussian with
Manuscript received January 03, 2011; revised March 25, 2011; accepted March 31, 2011. Date of publication May 12, 2011; date of current version June 15, 2011. The authors are with the Faculty of Applied Sciences, Delft University of Technology, Mekelweg 15, 2629 JB Delft, Netherlands (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNS.2011.2141683
Fig. 1. The operation principle of a photomultiplier tube, Photon 1 creates a photoelectron at the photocathode that creates secondary electrons at the first dynode. Photon 2 creates a photoelectron at the photocathode that is back-scattered at the first dynode to the next dynode without making secondary electrons. Photon 3 transmits trough the photocathode to create one photoelectron at the first dynode.
in addition an exponential function to account for small amplitude pulses from the dynodes of the PMT. from In this work we will introduce a method to obtain recorded pulse height spectra in stead of approximating by an analytical function. We will utilize a pulsed light source where the average number of photons detected by the PMT per pulse can be varied from much smaller than one to several 1000. We studied three different PMTs. The small amplitude dynode pulses, approximated by an exponential by Dossi et al. [2], appear for our tubes as a clear band in the pulse height and should spectra. They have a significant contribution to be taken into account for absolute calibration of detected light pulses. II. THEORY AND EXPERIMENTAL METHODS Fig. 1 illustrates the operation principle of a photomultiplier tube. Ideally a single photon absorbed in the photocathode liberates one photoelectron to the vacuum of the tube that is then accelerated towards and focused on the first dynode. A number, , of secondary electrons are emitted from the first dynode that go further in the multiplication process eventually delivering a charge pulse at the anode output. The secondary emission factor for each dynode is subject to Poisson statistics and this leads in the anode output [4], [5] to a fractional variance
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(1)
DE HAAS AND DORENBOS: METHODS FOR ACCURATE MEASUREMENT OF THE RESPONSE OF PHOTOMULTIPLIER TUBES
where is the number of dynodes in the PMT and the mean dynode. secondary emission factor at the Instead of being absorbed by the photocathode, photons may transmit through it to produce one photoelectron at the first dynode [6], [7]. A photoelectron from the cathode can also be inelastically back-scattered by the first dynode [8]. Those types of photoelectrons do not undergo the full multiplication of the electron multiplier; the difference being . It results in a larger fractional variance in the anode output than given by (1). In addition to these photoelectron generated events we also have to deal with dark noise electrons that are liberated by the field effect or by thermionic emission from the cathode or the dynode material into the vacuum of the tube. Finally we have the electronic noise contribution in the pulse height spectrum. In of the PMT response order to have an accurate spectrum to detection of a single photon we should take all those contributions into account. A. Weak Light Pulses and Single Electron Response To derive the response of a PMT to the detection of a single photon, pulse height spectra were measured using a LED pulser operating at various pulse intensities. When a pulse of light is incident on a PMT, the number of detected photons is determined by Poisson statistics. With the average number of detected photons per LED pulse, the distribution in that number is given by
(2) We will denote the normalized pulse height spectrum of the anode output signals due to the repeated detection of one single where is the channel number. is the photon as normalized pulse height spectrum of repeated simultaneous detection of two photons. It is theoretically the same as the mathwith itself. Generalizing, we obematical convolution of tain the following relation for
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and are significant and very weak pulses only contains a large contribution from . We will show contributes only to the lower channel number part of that . The higher channel number part then provides us with . By using more intense pulses with the contribution from becomes small and the contribution of larger , decreases. We now have contributions from , but also a contribution from and depending on possibly other contributions. These spectra all contribute to the high . By combining the high channel channel number part of number part of the first recorded spectrum with the low channel number part of the second one we can reconstruct the sought . Spectrum can be measured with zero spectrum light pulse intensity. Once these two spectra are known, one may accurately determine the intensity of weak light pulses by using in (4) as a fitting parameter to the recorded pulse of those weak light pulses. This method heights spectrum appears to work quite satisfactory as long as is not too large, say smaller than about 8. B. Bright Light Pulses When the average number of detected photons per light pulse increases above a fiting by (4) is not practical anymore. It is better to employ two other methods. In the method of Bertoof laccini et al. [1] (method 1) the mean channel number the peak in the pulse height spectrum that is from the detection of the light pulses is compared with the mean channel . is now obtained number of the single photon response with (5) and are the values for the total electronic gain of where and . Eq. (6) can the two amplifiers used to record be used to calculate and .
(6) (3) where denotes the mathematical convolution of the two functions. Once we know we can calculate with (3) the PMT response to any number of detected photons. Here we assume that the gain of the PMT is independent off . For real light pulses fluctuates from pulse to pulse according to Poisson statistics. The pulse height spectrum of the anode output is then given by (4) where where for convenience the summation is stopped at becomes vanishingly small, T is the accumulation is the normalized time and the LED pulse frequency. dark count spectrum of the PMT that is obtained when the LED pulser is switched off. Our first aim is to derive the two unknown spectra and from recorded pulse height spectra . By using
where the summation is over all channels in the spectrum. Method 2 is based on the fractional variance in the pulse height spectrum of the detected light pulses, . is now obtained with
(7) where is the fractional variance in [4], [5]. The equation for the fractional variance of a pulse height spectrum is given by
(8) spectrum For both methods to determine an accurate is needed. The method of Bertolaccini et al. works satisfactorily provided that we have a good relative gain calibration of the
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Fig. 2. A scheme of the measurement setup used to record pulse height spectra of a pulsed LED light source. The graphic shows the timing of the gate pulse with respect to the spectroscopic amplifier output pulse.
amplifiers used. However, very often in literature the spectrum is not accurately recorded, and simply the channel number of the maximum in the spectrum is used for the mean value . This may easily lead to 10–20% error in the found value for [2]. Method 2 can only be used for stable light pulses where the variance in the number of detected photons is due to Poisson statistics only. Pulses from scintillation crystals do not obey this criterion. The variance is much augmented due to inhomogeneities in the crystal and due to the so-called nonproportional response contribution [5]. Moszynski et al. [10] adopted a method where the pulse is calibrated by means of a light pulser. height spectrum The LED light pulse intensity is adjusted until the peak in the spectrum is at the channel number where also the peak of the scintillation pulses is located. Eq. (7) can then be used to calculate from the width of the LED peak in the spectrum. The advantage of this method over method 1 is that we do not need to accurately calibrate the electronic gains used for recording the spectra. III. EXPERIMENTAL METHODS We have used a method that was also employed by Bellamy et al. [3] and Dossi et al. [2] to measure the response of a PMT to light pulses. The method is illustrated in Fig. 2. A PicoQuant PLS370 LED head is used as pulsed light source. It is operated . The LED emits at a constant pulse frequency of 377 nm photons in a 10 nm full width at half maximum intensity (FWHM) wide band, and with sub nanosecond duration. The intensity of the light pulse can be attenuated electronically by means of the LED head hardware. The light pulses transmitted through a diffuser are incident on the photocathode of the PMT where they illuminate an area of about 25 mm. We tested three types of PMTs, all with a diameter of 51 mm. A Hamamatsu R1791 (SN LA0028) PMT with a boxand-grid dynode structure which has a good performance for scintillation counting was tested. We employed a homemade
voltage divider that utilizes only the first five dynodes for electron multiplication [9]. Also two Super Bialkali R6231-100 (SN ZE4500 and ZE4503) Hamamatsu PMTs with a box-and-linear 8-stage dynode structure with standard E1198-26 voltage divider were tested. These latter two PMTs are high quantum efficiency PMTs brought to the market by Hamamatsu few years ago. The anode output of the PMT was fed to a Cremat preamplifier and an Ortec 672 spectroscopy amplifier (SA). Note that the combined gain of the two amplifiers appears as in (5). Two Cremat preamplifiers were used; a CR-110 type with a large gain for small anode signals and a CR-112 with a relatively small gain for large signals. A spectroscopic shaping time of 0.5 was used for all studies. We gated the Ortec AD114 ADC synchronous with the LED pulses, and therefore only the anode charge pulses synchronous with the LED pulse are further processed. The graphic in Fig. 2 shows how the 0.9 wide gate pulse is positioned over the Gaussian output from the spectroscopy amplifier. By minimizing the gate width the dark count rate will reduce strongly. The ADC requires that the peak of the input pulse arrives after the gate has opened and the gate has to extend to at least 0.5 after the peak. Such setting of the gate did however distort the signals that were counted in the first 20 channels of the ADC output histogram. We solved this by increasing the width of after the peak. Each gate pulse will produce the gate to 0.7 . That can be detected a count in the recorded spectrum photons from the LED, or when no photon is detected either a dark event is registered or simply the electronic noise at the ADC input. IV. RESULTS AND DISCUSSION In the following we will first accurately determine both and . Next we will demonstrate that by fitting the recorded of weak light pulses using (4) we pulse height spectrum obtain the unknown average intensity of these pulses. This method works well for . For brighter pulses with we use the two other methods to determine described is Section II-B. A. Calibration of PMTs Using Weak Light Pulses Fig. 3(a) shows a set of pulse height spectra as function of the LED pulse intensity, i.e., as function of , and recorded with the R1791 PMT, with a pulse frequency of 10 kHz and a . In order to have output anode measuring time of pulses well above the electronic noise levels, these spectra were recorded with a relative high PMT supply voltage. Spectrum 5 dark noise spectrum recorded with zero light pulse is the intensity. The dark noise consists of three contributions. 1) Zero amplitude detections which means that the ADC does not detect an event within the gate width. It occurs in 89% of the gate events. 2) Electronic noise appears as the half-Gaussian profile below channel 20 in Fig. 3(b). It occurs in 10% of the gate events. 3) The true dark noise events from the PMT account for 1% of the recorded events. Spectrum 1 is recorded with a weak pulse intensity where of two photon detection is very small. the probability The Gaussian shaped band with a maximum around channel 510
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0
0900 V with varying intensity of the LED pulses. The fitted values for are
Fig. 4. The normalized response f (x) of the R1791 PMT at HV = 900 V to the detection of single photons. The shaded part illustrates the contribution from the first dynode.
is due to single photoelectrons from the photocathode that undergo the full multiplication of the electron multiplier. We will denote this band as the cathode-band. When the light pulse intensity is further increased, a second band develops in spectrum 2 with a maximum near channel 1040. This band is due to the creation of two photoelectrons from the cathode. The band becomes more pronounced when the pulse intensity increases further, see spectra 3 and 4. Bands from the simultaneous detection of three or even more photons are also present; however they are located beyond channel 1500 and not shown in Fig. 3. Fig. 3(b) gives an enlarged view of the first 100 channels of spectra 1 to 4 in Fig. 3(a). The half-Gaussian profile below channel 20 is due to electronic noise and is part of the dark noise . Above , we observe a clear band with spectrum . This band is attributed to photoa maximum around electrons from the first dynode [6], [7] or photoelectrons from the cathode that are inelastically back scattered from the first dynode [8], see Fig. 1. We will therefore denote this band as the , see spectrum 5 dynode-band. The dark noise spectrum in Fig. 3(a), shows in the first 20 channels the electronic noise events. The counts in channels 20 to 80 are attributed to dark noise events generated by electrons from the first dynode of the PMT. The contribution from cathode noise near channel 500 is very small. , has only a significant value for and For and then according to (4) only and contribute . If increases then will decrease and the conto to the spectrum decreases accordingly. This tribution of effect is demonstrated in Fig. 3(b). In spectrum 1 we observe for is that the electronic noise component from much more intense than the dynode-band. With increase of light pulse intensity the electronic noise contribution decreases proand it is minimum for spectrum 4. portional with by combining We now compose the sought spectrum the part of spectrum 4 between channels 20 and 400 with the part of spectrum 1 between the channels 150 and 1500. The first part provides the best representation of the dynode band and the
second part of the cathode band. The two partial spectra were scaled to have maximum overlap between channel 150 and 400. The electronic noise contribution in spectrum 4 was removed by a simple extrapolation of the dynode band towards as illustrated by the dotted curve in Fig. 3(b). This extrapolation may seem somewhat arbitrary, but its precise shape is not crucial spectrum, i.e., for what follows in this work. The resulting the PMT response to the detection of single photons, is shown in Fig. 4. By fitting (4) to the spectra 1, 2, 3, and 4 in Fig. 3 by using and , we obtained for values of 0.02, 0.14, 0.31, and 0.35 detected photons/light pulse, respectively. Eq. (2) then for each recorded spectrum. We have obtained gives us the normalized spectra in Fig. 3 by dividing each recorded spec. contributes then equally strong to each trum by spectrum. This is the reason that the cathode bands of spectra 2 to 4 overlap so nicely. Fig. 3 shows that the ratio between the number of counts in the cathode-band to that in the dynode-band is independent of pulse intensity . From this observation we . The conclude that the dynode-band is a genuine part of cathode band in Fig. 4 can be approximated by a Poisson distribution enabling the separation of the cathode and dynode contributions from one another. The total number of counts in the dynode-band, shown as the shaded part in Fig. 4, is about 19% of that of the entire spectrum. Our conclusion is that 19% of detected photons create a photoelectron that will not be fully multiplied in the electron multiplier of the R1791 PMT. Fig. 5 demonstrates the quality of the fit of (4) to the various spectra measured with the R1791 PMT. The figure shows spectra of weak light pulses together with the main contributing spectra. For we observe three separate bands in . The first band near channel 80 is due to events where both photons are detected in the dynode-band, for the second band or shoulder at channel 560 one photon is detected in the dynode-band and the other in the cathode-band, and for the last band at channel 1020 both photons are detected in the cathode values of the three fits in Fig. 5 are close band. The reduced to one, showing that the model fits well to the experimental data. This same method was used before by Dossi et al. [2] and Bellamy et al. [3]. There is one important difference with our
Fig. 3. a) Pulse height spectra recorded with the R1791 PMT at
HV =
0.02, 0.14, 0.31, 0.36, and zero detected photons/pulse for spectra 1 through 5, respectively. Spectra 1 to 4 are normalized by division with P (1; ). b) Enlarged view of the first 100 channels to better reveal the dynode-band and dark (electronic) noise contributions.
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Fig. 5. Pulses height spectra of LED pulses with a) is 0.2, b) is 1.3 and c) is 2.3. The measured spectrum in black and the fitted spectrum in red fully overlap each other. The separate contributing functions f (x) are shown in blue.
Fig. 6. Pulse height spectra recorded with the R6231-100 SN = ZE4503 PMT at HV = 675 V with varying intensity of the LED pulses. The fitted values for are 0.02, 0.07, 0.35, 0.87 and zero detected photons/pulse for spectra 1 through 5, respectively. Spectra 1 to 4 are normalized by division with P (1; ).
method. Our spectrum is a measured spectrum that contains a clear dynode-band. In the work by Dossi et al. [2] a spectrum was used with a Gaussian shaped cathode-band and an estimated exponential shape for the dynode-band. Bellamy et al. [3] employed a Gaussian shaped cathode-band only. We also tested the two Super Bialkali Hamamatsu R6231-100 PMTs with serial numbers ZE4500 and ZE4503. The same set of experiments as for the R1791 PMT was performed. Spectra 1, 2, 3 and 4 in Fig. 6 are pulse height spectra of the LED light pulses as function of increasing pulse intensity measured with . We tube ZE4503. Spectrum 5 is the dark noise spectrum now observe a clear cathode dark noise band with maximum at channel 640 that is attributed to field emission and thermionic noise from the photocathode. The band peaking near channel 40 is the dynode-band. Compared with the cathode and dynode of R1791, a 15 times higher cathode and noise part of dynode dark count rate is observed. But it is still less than 1% . of the total number of counts in With a procedure similar as performed for the R1791 spectra, of the ZE4503 PMT has been composed the spectrum by joining the part between channels 10 and 950 of spectrum
IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 58, NO. 3, JUNE 2011
Fig. 7. The normalized response f (x) of the R6231-100 PMTs. Spectrum 1) serial number ZE4500 and spectrum 2) serial number ZE4503.
3 with the part between channels 900 and 1500 of spectrum 2. The electronic noise contribution was removed by methods similar as for the R1791 PMT. By fitting (4) to the measured spectra, the values for were first determined. Next, the spectra , and those spectra were normalized by dividing with are shown in Fig. 6. Different from the results for R1791, the spectra 1 to 3 of Fig. 6 do not have the same number of counts at the maximum of the cathode-band. This is caused by the 15 contribution to especially times larger dark noise at low value for . For spectra 3 and 4, where is larger and reduced, both spectra have the same the contribution of number of counts at the maximum of the cathode and dynode band. for the two Fig. 7 shows the obtained functions R6231-100 PMTs. Although the general appearance is similar of R1791, there are two important differences. 1) to The dynode-band of R6231-100 is more intense and narrower than that of R1791. About 20% of counts are in the dynode band which is about the same as for R1791. 2) There is a tail spectra of the extending to beyond channel 1500 in the R6231-100 PMTs that is not observed for R1791. The origin of the tail is not yet clear. In any case, it is not caused by the simultaneous detection of two photons because the contribution does not disappear for low LED pulse intensity when is negligible. B. Calibration of PMT’s Using Bright Light Pulses Bright scintillators like emit intense and short duration scintillation pulses. To avoid non-linearity in the gain of the PMT due to too high peak anode or peak cathode currents one needs to operate the PMT at relatively can low supply voltage [9]. Under those conditions not be measured accurately. However, the mean value and can still be obtained using the fractional variance of two methods described in Section II-B. First, we recorded a pulse height spectrum of relatively intense LED pulses at the were obtained. These spectra same HV where the specra are shown for the R1791 PMT at 900 supply voltage in and as calculated with (6) are Fig. 8. The mean values indicated in the spectra. With (8) the fractional variances in both spectra are obtained. The mean number of detected LED
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TABLE I THE MEAN CHANNEL NUMBER AND VARIANCE OF ( ) OF R1791 IS SHOWN IN COLUMNS 5 AND 6, OF R6231-100 ZE4500 IN COLUMNS 11 AND 12 AND OF R62310-100 ZE4503 IN COLUMNS 17 AND 18 AS FUNCTION OF HV. COLUMNS 4, 10, AND 16 SHOW THE CHANNEL NUMBER OF THE CATHODE BAND MAXIMUM OF ( ). THE MEAN NUMBER OF DETECTED PHOTON OF THE USED LED PULSE CALCULATED WITH THE AND THE VARIANCE METHOD ARE COMPILED IN COLUMN 2 AND 3, 8 AND 9, AND 14 AND 15 METHOD OF BERTOLACCINI
m
x
v
f x
f x
0
Fig. 8. Two measured spectra with the R1791 at HV = 900 Volt. ( ) spectrum at a SA gain of = 200 giving a) The measured = 448 and = 0 22. b) A measured laser pulse spectrum at a SA = 10 giving = 629 and = 0 0437. gain of
m
g
f x v :
m
v
:
g
photons can now be determined. The method of Bertolaccini and the fractional variance method gives et al. gives , see Table I. This demonstrates that the LED is a stable light source where the variance in the number of detected photons is due to Poisson statistics only. Next, while constant, the HV supply keeping the LED intensity, i.e., is stepwise reduced and each time the pulse height spectrum is recorded. Using (8) and (6) then provides and . Finally with (7) and (5) the fractional variance and of as function of the supply voltage are the mean obtained. The results for the R1791 and the two R6231-100 PMTs are compiled in Table I. The first row shows results measured at and the highest supply voltages where both spectra were recorded for all three tubes. The number of detected phoand method 2 tons per LED pulse determined by method 1 are always close to each other. The position of the cathode, and the fractional variband , the mean channel number ance of is compiled for each tube. The fractional variance of the high quantum efficiency R6231-100 PMTs appears significantly larger than that of R1791. The other three rows in and at various the Table show the obtained values for supply voltages. We observe that for all three tubes the fracis tional variance does not change with the supply voltage. proportional with the gain of the PMT and decreases with decreasing supply voltage. Because we used only five dynodes of
the R1791 PMT, the gain of that PMT changes only a factor of 8.5 when the supply voltage is lowered from 900 V to 500 V. One may use the results in Table I to determine the average number of photons detected from relatively bright pulses, like scintillation pulses in gamma ray spectroscopy. Let us consider the detection of 662 keV gamma ray photons with a scintillation crystal. The pulse height spectrum will show the so called total absorption peak due to events where the total energy of 662 keV has been depostited in the scintillator. At the supply can not voltae used the single photon response spectrum values be recorded accurately and we have to employ the from Table I. If the PMT and the relative gain of the preamplifier and spectroscopy amplifiers are well calibrated (5) gives us , i.e. the number of photoelectrons generated per 662 keV deposited energy. V. SUMMARY By means of 10 kHz LED pulses of which the intensity was varied by three orders of magnitude, we accurately determined the response of PMTs to the detection of one single photon. It appears that almost 20% of the detected photons create photoelectrons that do not undergo the full multiplication of the PMT. This has large affect on the average channel number and the fractional variance of the single photon response spectrum. The accurate response spectrum of single photons has been used to fit the pulse height spectra of light pulses of unknown intensity. Equation (4) provides excellent fits where the only parameter is the average number of detected photons of the unknown intensity light pulse. The method works particularly well for , and is therefore a good method to determine the intensity of weak light pulses. For brighter pulses with two other methods were used to determine brightness. The traditional method of Bertolaccini et al. based on the average channel of pulse height spectra and a method based on the fractional variance of the spectra. The values obtained from both methods are consistent with each other and this confirms that the found single photon spectra are correct. The advantage of the fractional variance method is that there is no need for a relative gain calibration of the electronic amplifiers used for recording pulse height spectra. This work also revealed details on the performance of the two types of Hamamatsu PMTs tested. The high quantum efficiency R6231-100 PMTs show 15 times higher dark count rate than the R1791 PMT, and also the fractional variance in the appears larger. single photon response spectrum
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REFERENCES [1] M. Bertolaccini, S. Cova, and C. Bussolati, in Proc. Nuclear Electr. Symp., Versailles, France, Sep. 10–13, 1968, pp. 8-1–8-13. [2] R. Dossi, A. Ianni, G. Ranucci, and O. J. Smirnov, “Methods for precise photoelectron counting with photomultipliers,” Nucl. Instrum. Methods Phys. Res. A, vol. 451, pp. 623–637, 2000. [3] E. H. Bellamy, G. Bellettini, and J. Budagov et al., “Absolute calibration and monitoring of a spectrometric channel using a photomultiplier,” Nucl. Instrum. Methods Phys. Res. A, vol. 339, pp. 468–476, 1994. [4] J. B. Birks, The Theory and Practice of Scintillation Counting. New York: Pergamon, 1967. [5] P. Dorenbos, J. T. M. de Haas, and C. W. E. van Eijk, “Non-proportionality in the scintillation response and the energy resolution obtainable with scintillation crystals,” IEEE Trans. Nucl. Sci., vol. 42, no. 6, pp. 2190–2202, Dec. 1995.
[6] G. Montarou, M. Crouau, P. Grenier, S. Poirot, and F. Vazeille, Characterization of 8-Stages Hamamatsu R5900 Photomultipliers for the TILE Calorimeter TILECAL-No-25, Sep. 1997. [7] A. G. Wright, “Method for the determination of photomultiplier collection efficiency, F,” Appl. Opt., vol. 49, pp. 2059–2065, 2010. [8] “Photomultiplier tubes, principle and applications,” pp. 2–9, Photonis Imaging Sensors, Merignac, France, 2002. [9] P. Dorenbos, J. T. M. de Haas, and C. W. E. van Eijk, “Gamma ray spectroscopy with a 19 diameter 19 mm LaBr : 0:5%Ce scintillator,” IEEE Trans. Nucl. Sci., vol. 51, no. 3, pp. 1289–1296, Jun. 2004. [10] M. Moszyn´ski, T. Szcz´en´iak, and M. Kapusta et al., “Characterization of scintillators by modern photomultipliers—A new source of errors,” IEEE Trans. Nucl. Sci., vol. 57, no. 5, pp. 2886–2896, Oct. 2010.
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